348                                                                        IEEE TRANSACTIONS ON MOBILE COMPUTING,         ...
HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION            ...
350                                                                              IEEE TRANSACTIONS ON MOBILE COMPUTING,   ...
HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION            ...
352                                                                     IEEE TRANSACTIONS ON MOBILE COMPUTING,            ...
HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION            ...
354                                                                         IEEE TRANSACTIONS ON MOBILE COMPUTING,        ...
HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION            ...
356                                                            IEEE TRANSACTIONS ON MOBILE COMPUTING,           VOL. 9,   ...
HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION            ...
358                                                              IEEE TRANSACTIONS ON MOBILE COMPUTING,         VOL. 9,   ...
HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION            ...
12. power control and channel allocation in cognitive radio networks with primary users’ cooperation
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12. power control and channel allocation in cognitive radio networks with primary users’ cooperation

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12. power control and channel allocation in cognitive radio networks with primary users’ cooperation

  1. 1. 348 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 9, NO. 3, MARCH 2010 Power Control and Channel Allocation in Cognitive Radio Networks with Primary Users’ Cooperation Anh Tuan Hoang, Member, IEEE, Ying-Chang Liang, Senior Member, IEEE, and Md Habibul Islam, Member, IEEE Abstract—We consider a point-to-multipoint cognitive radio network that shares a set of channels with a primary network. Within the cognitive radio network, a base station controls and supports a set of fixed-location wireless subscribers. The objective is to maximize the throughput of the cognitive network while not affecting the performance of primary users. Both downlink and uplink transmission scenarios in the cognitive network are considered. For both scenarios, we propose two-phase mixed distributed/centralized control algorithms that require minimal cooperation between cognitive and primary devices. In the first phase, a distributed power updating process is employed at the cognitive and primary nodes to maximize the coverage of the cognitive network while always maintaining the constrained signal to interference plus noise ratio of primary transmissions. In the second phase, centralized channel assignment is carried out within the cognitive network to maximize its throughput. Numerical results are obtained for the behaviors and performance of our proposed algorithms. Index Terms—Wireless communications, dynamic spectrum access, distributed control, joint power control and channel allocation. Ç1 INTRODUCTIONT HEtraditional approach of fixed spectrum allocation to licensed networks leads to spectrum underutilization.In recent studies by the FCC, it is reported that there are radio network. The objective is to maximize the total throughput for the cognitive network while maintaining a required signal to interference plus noise ratio (SINR) forvast temporal and spatial variations in the usage of all primary receivers (PRXs).allocated spectrum, which can be as low as 15 percent [1]. We consider both downlink and uplink scenarios in theThis motivates the concepts of opportunistic spectrum access cognitive network. For the downlink control scenario, wethat allows secondary cognitive radio networks to oppor- propose a two-phase downlink mixed distributed/centra-tunistically exploit the underutilized spectrum. In fact, lized control algorithm (DL-MDCA) that requires minimalopportunistic spectrum access has been encouraged by both cooperation between cognitive and primary devices. In therecent FCC policy initiatives and IEEE standardization first phase of DL-MDCA, BS and primary transmittersactivities [2], [3]. (PTXs) participate in a distributed power updating process On one hand, opportunistic spectrum access can im- that strives to maximize the coverage of the cognitiveprove the overall spectrum efficiency. On the other hand, network. BS and PTXs need to exchange simple controltransmission from cognitive devices can cause harmful signaling to initiate and terminate this power updatinginterference to primary users of the spectrum. This process. Apart from that, no further control informationmotivates our objective of maximizing the throughput of a needs to be exchanged between BS and PTXs. In the secondcognitive radio network while maintaining performance of phase of DL-MDCA, based on the coverage obtained fromcoexistent primary users. the first phase, BS allocates channels to different CPEs in In this paper, we consider a point-to-multipoint cogni- order to maximize the total downlink transmission rate.tive radio network in which a base station (BS) controls This is achieved by formulating and solving a maximumand supports a set of fixed-location customer premise weighted bipartite matching problem. For the uplinkequipments (CPEs). The spectrum of interest is divided control scenario, a similar two-phase control algorithm,into a set of nonoverlapping, independent channels. Some called UL-MDCA, is proposed. In the first phase, distrib-of these channels are used by a set of point-to-point uted power control is carried out between PTXs and CPEs.primary transmissions. We are interested in the power In the second phase, centralized channel assignment iscontrol/channel assignment problem for the cognitive applied within the cognitive network. It can be noted that, in our proposed system, secondary. The authors are with the Institute for Infocomm Research, A-STAR, nodes exercise “cognition” when intelligently adapting 01 Fusionopolis Way, #21-01 Connexis, Singapore 138632. their transmit power such that their SINR constraint is E-mail: {athoang, ycliang, habibul}@i2r.a-star.edu.sg. met while not violating the SINR constraint of the primaryManuscript received 8 Aug. 2008; revised 4 Feb. 2009; accepted 1 May 2009; links. This is consistent with the concept of dynamicpublished online 29 July 2009. spectrum access based on constraint in interference tem-For information on obtaining reprints of this article, please send e-mail to:tmc@computer.org, and reference IEEECS Log Number TMC-2008-08-0313. perature [4]. In traditional priority-based network, second-Digital Object Identifier no. 10.1109/TMC.2009.136. ary devices are normally allowed to transmit only when the 1536-1233/10/$26.00 ß 2010 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS
  2. 2. HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION 349higher priority devices are not transmitting. To implementour proposed system, there should be some mechanisms forcognitive nodes to sense the channels and detect primaryusers. This can be done using different spectrum sensingtechniques such as matched filter, energy detector, andcyclostationary feature detector [5], [6], [7], [8]. The rest of the paper is organized as follows: Workrelated to this paper is described in Section 2. In Section 3,we describe the system model, introduce important nota-tion, and discuss the operation principles of the cognitiveand primary networks. The problem of power control/channel assignment to maximize the downlink throughputof the cognitive radio network is considered in Section 4.Particularly, the DL-MDCA scheme is proposed and someimportant characteristics of this algorithm are discussed. InSection 5, the uplink control scenario is considered and thecontrol algorithm UL-MDCA is proposed. In Section 6, weprovide analysis of the complexity of DL-MDCA and Fig. 1. Deployment of a cognitive radio network. The cognitive networkUL-MDCA. To facilitate the study of DL-MDCA and consists of one BS serving multiple fixed-location CPEs. The primaryUL-MDCA, in Section 7, we introduce some simpler control network is modeled as a set of point-to-point PTX-PRX links.algorithms. Numerical results showing the behaviors andperformance of our proposed schemes are presented in a node is beyond a certain distance from a primary user,Section 8. Finally, we conclude the paper and outline future then no harmful interference will be caused. The channelresearch directions in Section 9. allocation problems in [14], [15] are then formulated as graph coloring problems. The problem in [16] is solved via integer linear programming.2 RELATED WORK Our paper is also related to [17] and [18], where aIn our previous work [9], [10], [11], we consider related problem of joint channel assignment and transmit powerproblems of centralized power/channel allocation to max- control for multichannel wireless ad hoc networks isimize the number of users supported in multichannel considered. As the work is not for cognitive radio,cognitive radio networks. However, [9], [10], [11] only focus protecting primary users is not of concern. In a broaderon the downlink scenario and assume that primary users do context, our paper is related to work on conventionalnot cooperate with the cognitive radio users in any way. This problem of power control in cellular networks such as [19],paper considers both downlink and uplink scenarios and [20], [21]. Compared to this related work, the problemhighlights the significant benefits when primary users considered in this paper is different due to the need tocooperate with cognitive users in a simple, distributed protect primary users and the joint control over multiplemanner. In [12], the authors study problems of secondary channels. In our system model, different primary users mayspectrum access with minimum SINR guarantee and inter- transmit and receive on different channels. The channelference temperature constraint. They consider both scenar- usage pattern of primary users, coupled with their loca-ios, when all the secondary links can be supported and when tions, makes the spectrum available for cognitive usagenot all the secondary links can be supported with their SINR irregular. This kind of spectrum irregularity, across availablerequirement. In the first scenario, the control objective is to channels and BS-CPE links, makes it necessary to carry outmaximize the total transmission rate of the secondary users, channel assignment and power control jointly for allwhile in the second scenario, an access control problem also channels in order to achieve a good system throughput.needs to be dealt with. A control problem similar to [12] isalso studied in [13]. We note that, unlike this paper, in both[12] and [13], no cooperation from primary users is assumed. 3 SYSTEM MODELFurthermore, [12], [13] focus on single-channel scenario, and We consider an opportunistic spectrum access scenario astherefore, channel allocation is not of concern. depicted in Fig. 1. The spectrum of interest is divided into Other works that consider channel assignment for K channels that are licensed to a primary network ofmultichannel cognitive radio networks include [14], [15], M PTX-PRX links. Each of the M PTX-PRX links occupies[16]. In [14], Wang and Liu consider a problem of one of the K channels (this implies M K). In the sameopportunistically allocating multiple licensed channels to area, a secondary cognitive radio network is deployed. Thisa set of cognitive stations so that the total number of cognitive network consists of a BS serving a set of N CPEschannel usages is maximized. In [15], Zheng and Pengconsider a similar problem and introduce a reward function by opportunistically making use of the K channels. Wethat is proportional to the coverage areas of base stations. consider both downlink (from BS to CPEs) and uplink (fromThey also allow the interference effect to be channel specific. CPEs to BS) scenarios in the secondary cognitive network.The problem in [16] is for a cognitive-radio, multihop We assume that the BS can transmit and receive on up towireless network. It should be noted that transmit power K channels at a time while each CPE can transmit or receivecontrol is not considered in [14], [15], [16]. Instead, on only one channel at a time. Furthermore, each channelprotection of primary users is based on physical separation can only be used by one CPE (in either downlink or uplink)of communication entities. In particular, it is assumed that if at a given time.
  3. 3. 350 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 9, NO. 3, MARCH 2010 TABLE 1 Important Notation and Acronyms3.1 Notation sd Similarly, let n;c denote the SINR experienced by CPE n.To facilitate further discussion, let us define the following sd n;ccan be calculated asnotation (see Table 1): sd P0;c Gss s 0;n;c n;c ¼ PM p ps ; 1 n N: ð2Þ . Gpp i;j;c denotes the channel gain from PTX i to PRX j No þ j¼1 Pj;c Gj;n;c on channel c, 1 i; j M, 1 c K. . Gss denotes the channel gain from secondary i;j;c 3.3 Uplink Scenario in Cognitive Network: SINR at node i to secondary node j on channel c. Here, we PRXs and BS denote BS as secondary node 0 and N CPEs as Consider the uplink scenario in the cognitive radio network. secondary nodes 1 to N, 0 i; j N. Assuming that CPE n (1 n N) is assigned to transmit on . Gsp denotes the channel gain from secondary i;j;c pu channel c and letting i;n;c denote the SINR experienced by node i to PRX j on channel c, 0 i N, 1 j M. pu PRX i, i;n;c can be calculated as . Gps denotes the channel gain from PTX i to i;j;c secondary node j on channel c, 1 i M, 0 j N. pu Pi;c Gpp p i;i;c p i;n;c ¼ PM ; 1 i M: ð3Þ . Pi;c denotes the transmit power of PTX i on channel c. No þ Pj;c Gpp þ Pn;c Gsp p s p j¼1;j6¼i j;i;c n;i;c If PTX i does not transmit on channel c, then Pi;c ¼ 0. su . s Pi;c denotes the transmit power of secondary node i At the same time, the SINR at BS, denoted by n;c , can be on channel c. If secondary node i does not transmit calculated as s on channel c, then Pi;c ¼ 0. su Pn;c Gss s n;0;c . No denotes the noise spectrum density at BS, CPEs, n;c ¼ PM p ps : ð4Þ and PRXs. Note that we assume the noise figure No þ j¼1 Pj;c Gj;0;c being the same for all receivers just for the sake of brevity. The results of the paper can be applied 3.4 Protecting Primary Users directly to the case when different receivers experi- We assume that, for appropriate performance of the ence different noise figures. primary network, the received SINR at each PRX must be above a predefined value of p . In particular, let Åc3.2 Downlink Scenario in Cognitive Network: SINR denote the set of all PRXs that receives on channel c, when at PRXs and CPEs the cognitive radio network operates in the downlinkConsider the downlink scenario in the cognitive radio scenario, we must have pdnetwork. For each channel c, let i;c denote the SINR pd pdexperienced by PRX i. i;c can be calculated as i;c ! p ; 8i 2 Åc : ð5Þ pd Pi;c Gpp p i;i;c When the cognitive radio network operates in the uplink i;c ¼ PM p pp ; 1 i M; ð1Þ scenario and CPE n is assigned to transmit on channel c, we No þ j¼1;j6¼i Pj;c Gj;i;c þ P0;c Gsp s 0;i;c must have swhere it should be noted that P0;c is the transmit power of BS pu i;n;c ! p ; 8i 2 Åc : ð6Þon channel c and Gsp is the channel gain from BS to PRX i. 0;i;c
  4. 4. HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION 351 To support the operation of the cognitive network, the X K an;c 1; 8n 2 f1; . . . ; Ng; ð13Þprimary network must be able to tolerate a certain level of c¼1interference from cognitive transmissions. We assume thatfor each channel c and PTX i transmitting on c, i.e., i 2 Åc , X Nthere exists a transmit power P~ such that p i;c an;c 1; 8c 2 f1; . . . ; Kg: ð14Þ n¼1 P~p Gpp i;c i;i;c PM ! p; 8i 2 Åc ; ð7Þ In (10), P s is the maximum transmit power for BS on each No þ j¼1;j6¼i P~ Gpp þ p j;c j;i;c channel, and in (11), P p is the maximum transmit power forwhere is a positive constant. Essentially, this assumption each PTX. These maximum powers can be regarded as themeans that, apart from the interference caused by other intrinsic limits for the type of secondary/primary devices,primary transmissions, each primary receiver can tolerate which are normally set out by spectrum regulators. Inequal-an extra interference, e.g., from secondary transmission, ity (12) is due to the SINR constraint for primary links.equal to . Inequality (13) is due to the fact that each CPE can only receive on one channel at a time and (14) is because two CPEs3.5 Transmission Rates for Secondary Connections cannot simultaneously share a single channel.Using adaptive coding and/or modulation, the transmis-sion rate between BS and each CPE (in either downlink or 4.1 General Approachuplink direction) can be varied according to the received As the K channels are independent of each other and theSINR. For a given channel, we assume that the transmission rate function fð:Þ is monotonically nondecreasing, withoutrate between BS and CPE with SINR of can be written as loss of optimality, the downlink throughput maximization problem can be separated into the following two phases: 0; if s ; uðÞ ¼ ð8Þ . Phase 1—Power Control: For each channel, find the fðÞ; if ! s ; maximum transmit power of BS, together with thewhere s is the SINR threshold below which no transmis- transmit powers of PTXs, so that the SINR constraintssion is possible between BS and CPEs. When the SINR is of all PRXs receiving on that channel are met. ! s , the corresponding downlink transmission can be . Phase 2—Channel Assignment: After Phase 1, givencarried out at rate fðÞ. Function fðÁÞ depends on various the maximum transmit powers of BS on K channels,factors such as available coding/modulation schemes and carry out channel assignment for N CPEs so that thebit error rate requirement. However, in all cases, fðÁÞ is total downlink transmission rate is maximized.monotonically nondecreasing. For Phase 1, one control option is to carry out centralized power calculation for BS and all PTXs. In our previous works in [9], [10], [11], we follow this approach and apply4 DOWNLINK THROUGHPUT MAXIMIZATION the Perron-Frobenious theorem ([22]) to obtain Pareto-In this section, let us consider the problem of power control optimal transmit power vectors. However, the centralizedand channel assignment to maximize the downlink power control approach requires knowledge of all channelthroughput of the cognitive radio network while protecting gains from BS to PRXs and from PTXs to CPEs. This meansK PTX-PRX links. The problem of maximizing the uplink a great deal of cooperation between primary and cognitivethroughput is considered in Section 5. networks. In this paper, we follow another power control Let an;c be a binary variable that indicates whether approach, which is carried out in distributed manner andchannel c is assigned to the downlink transmission from BS requires minimal cooperation between the two networks.toward CPE n. In particular, an;c is set to 1 if channel c is On the other hand, as Phase 2 only involves BS and CPEs, aassigned to the downlink transmission toward CPE n. centralized channel assignment scheme is appropriate. WeOtherwise, an;c is set to 0. The problem of power control/ term our control approach the Downlink Mixed Distrib-channel assignment to maximize the total downlink uted/Centralized Algorithm (DL-MDCA). Each phase oftransmission rate of the cognitive network can be stated as DL-MDCA is discussed below. XX À Á K N 4.2 Phase 1 of DL-MDCA: Distributed Power Control sd arg max u n;c an;c ; ð9Þ For Phase 1, we propose a synchronous downlink dis- s p P0;c ;Pi;c ;an;c c¼1 n¼1 tributed power updating (DL-DPU) process that strives tosubject to: maximize the coverage of BS while always guaranteeing the SINR constraint of all PRXs. The DL-DPU process is applied 0 s P0;c P s; 8c 2 f1; . . . ; Kg; ð10Þ to one channel at a time. For channel c, 1 c K, the following actions are carried out: p 0 Pi;c P p; 8i 2 Åc ; 8c 2 f1; . . . ; Kg; ð11Þ . Initialization: Either BS or one of the PTXs operating on channel c initiates the power updating process by broadcasting some special tone. All PTXs that pd i;c ! p ; 8i 2 Åc ; 8c 2 f1; . . . ; Kg; ð12Þ transmit on channel c, together with BS, must participate in the power updating process. PTX i,
  5. 5. 352 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 9, NO. 3, MARCH 2010 8i 2 Åc , and BS set their transmit powers to the iteration. So the power updating process will stop after at p s initial values of Pi;c ð0Þ and P0;c ð0Þ, respectively. s most dlog ðP sP ð0ÞÞe iterations. u t 0;c . Power updating: At step k, the following activities are p s Proposition 2. If the initial transmit powers Pi;c ð0Þ and P0;c ð0Þ carried out: 1) BS and PTXs transmit pilot signals at pd p ; 8i 2 Å , then pd ðkÞ ! s p the set power levels of P0;c ðkÞ and Pi;c ðkÞ, respectively. are selected such that i;c ð0Þ ! c i;c 2) PRXs estimate their SINR and feed back to their p ; 8k ! 1. corresponding PTXs. 3) PTX i and BS update their Proof. The proof is by induction. Suppose that for some transmit powers according to: pd k ! 0, i;c ðkÞ ! p . We have p p p Pi;c ðk þ 1Þ ¼ Pi;c ðkÞ pd ; i 2 Åc ; pd i;c ðk þ 1Þ ¼ i;c ðkÞ ð15Þ s s P0;c ðk þ 1Þ ¼ P0;c ðkÞ: Pi;c ðk þ 1ÞGpp p i;i;c ¼ PM p pp s sp pd No þ j¼1;j6¼i Pj;c ðk þ 1ÞGj;i;c þ P0;c ðk þ 1ÞG0;i;c Here, i;c ðkÞ is the SINR at PRX i after step k and can be calculated using (1). In addition, is a power Pi;c ðkÞ p =i;c ðkÞGpp p pd i;i;c ! PM scaling factor, which is slightly greater than one. No þ j¼1;j6¼i Pj;c ðkÞGj;i;c þ P0;c ðkÞGsp p pp s 0;i;c . Termination: The DL-DPU process will be terminated p Pi;c ðkÞGpp p i;i;c if at least one of the following conditions is true: ¼ À PM Á pd i;c ðkÞ No þ j¼1;j6¼i Pj;c ðkÞGpp þ P0;c ðkÞGsp p j;i;c s 0;i;c - The SINR experienced by at least one of the Pi;c ðkÞGpp p p i;i;c PRXs goes below the threshold p . ! PM - At least one of the transmitters (BS and PTXs) i;c ðkÞ No þ j¼1;j6¼i Pj;c ðkÞGpp þ P0;c ðkÞGsp pd p j;i;c s 0;i;c has its transmit power that approaches the p pd maximum transmit power constraint. ¼ pd i;c ðkÞ ¼ p: i;c ðkÞ A node can terminate the DL-DPU process by ð16Þ broadcasting some special tone (control message). We assume that the special tone to initiate Phase 1 is Note that the first inequality in (16) follows frombroadcasted on the same channel c. This can be achieved byperiodically reserving small time slots so that primary orcognitive nodes can broadcast the tone. During these time p p p p Pj;c ðk þ 1Þ ¼ Pj;c ðkÞ pd Pj;c ðkÞ; 81 j M; ð17Þslots, all nodes will not carry out normal data transmission. j;c ðkÞNodes that wish to broadcast the special initiating tone in aparticular reserved time slot can do so in a random access and the last inequality in (16) follows from 1. u tmanner, e.g., using p-persistent random access or schemesimilar to contention-based ranging in IEEE 802.16 [23]. This Proposition 2 states that if we start with the initialhelps avoid collisions of multiple concurrent tones. It is transmit powers for BS and all PTXs so that the SINRimportant to note that due to the simple nature of the tone, constraints of all PRXs are met, then during the powerthe overhead of reserving time slots to broadcast the tone updating process, the SINR constraints of all PRXs areshould be negligible. always maintained. Based on (7), we can set Pi;c ð0Þ ¼ P~ . p p i;c s When one node transmits the tone to initiate the power Then, if P0;c is set to a sufficiently small value such thatupdating process, it forces other nodes to cease normal P0;c Gsp , from (7), we will have i;c ð0Þ ! p ; 8i 2 Åc . In s 0;i pdcommunication to participate in the power updating process. case the SINR constraint of a PRX is violated at initializationThis can affect the primary and secondary performances, (e.g., due to the change in channel condition), the powerespecially in mobile environment when frequent power updating process will be immediately terminated. The BSupdates need to be carried out. To keep this negative effect then can further reduce its initial power level in subsequentunder control, one or a combination of the following power updating process.approaches can be employed: 1) a restriction can be set so Proposition 3. The SINR experienced by each CPE increasesthat only primary users can transmit the tone to initiate the after each power updating step.power updating process; 2) we can also set the limit on how Proof. Using (2), for 1 n N, we havefrequent the power updating process can be carried out. As can be seen from (15), PTX i updates its transmit P0;c ðk þ 1ÞGss s 0;n;c sdpower to aim at the SINR value of p . On the other hand, n;c ðk þ 1Þ ¼ PM p No þ i¼1 Pi;c ðk þ 1ÞGps i;n;cBS keeps on increasing its transmit power in order toincrease the cell coverage. A pseudocode for the DL-DPU P0;c ðkÞGss s 0;n;c ! P ð18Þprocess is given in Fig. 12. Next, let us prove some No þ M Pi;c ðkÞGps i¼1 p i;n;cimportant properties of the proposed DL-DPU process P0;c ðkÞGss s 0;n;c sdProposition 1. The DL-DPU process will be terminated after a P ¼ n;c ðkÞ; No þ M Pi;c ðkÞGps i¼1 p i;n;c finite number of iterations.Proof. The transmit power of BS starts from an initial value where the first inequality is due to (17) and the last s of P0;c ð0Þ and is increased by factor 1 after each inequality follows from 1. u t
  6. 6. HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION 353 In our DL-MDCA algorithm, Phase 1 of distributed power control does not require the assumption that each CPE only operates on one channel at a time. This assumption is used in Phase 2 to simplify the channel assignment process. How- ever, Phase 2 can also be readily extended to cover multiple- channel operation case. In particular, if each CPE can operate on up to L channels, then when forming the bipartite graph, we just need to represent each CPE by L vertices and the rest of the maximal matching operation is unchanged. It should also be noted that, when channels change, the SINR constraints for primary users can be violated. In that case, the primary users should send out warning tone and probably restart the power updating process.Fig. 2. Representing the coverage within one cell as a bipartite graph.The number on each link is its capacity. 4.4 Fairness ConsiderationsProposition 3 states that the coverage, i.e., number of CPEs It can be noted that by maximizing the transmit power ofthat BS can cover, is nondecreasing after each iteration. the BS, Phase 1 maximizes the set of CPEs that can be potentially assigned channels. Given that, how fair the4.3 Phase 2 of DL-MDCA: Centralized Channel channels are assigned to CPEs depends on specific Assignment algorithm in Phase 2. In this paper, we focus on throughputAfter the power updating process, for each channel c, BS has a maximization and achieve that with bipartite matching. On smaximum transmit power P0;c . Associated with this transmit the other hand, if the focus is fairness, we need to frequently reassign the channels. One way to do that is to divide the setpower are the SINRs experienced by N CPEs. The problem is of CPEs into multiple subsets, and consider these subsets inhow to assign K channels to different CPEs so that the total a round-robin manner. Given a particular subset of CPEs,downlink throughput is maximized. This is achieved by first we can then apply bipartite matching to maximize thetransforming the problem into a weighted bipartite matching achievable throughput for such subset.and then finding a maximal weighted match. The weighted bipartite graph is formed as follows: First,represent the N CPEs by a set of vertices, which is 5 UPLINK THROUGHPUT MAXIMIZATIONconnected to another set of vertices representing the K Now, let us consider the problem of power control/channelchannels. An edge exists between the vertex representing assignment for maximizing the uplink throughput of theCPE n and the vertex representing channel c if and only if, cognitive radio network. Similar to the downlink scenario,for channel c, the SINR at CPE n is not less than s . For each we propose a two-phase Uplink Mixed Distributed/edge, assign an weight that is equal to the corresponding Centralized Algorithm (UL-MDCA). In the first phase oftransmission rate calculated in (8). An example of such an UL-MDCA, distributed power control is carried out amongweighted bipartite graph is given in Fig. 2. CPEs and PTXs in order to meet their SINR constraints. In The problem of channel assignment to maximize the total the second phase of UL-MDCA, centralized channel assign-downlink transmission rate is equivalent to the problem of ment is applied within the cognitive network to maximizefinding a maximal matching for the corresponding the uplink throughput. It should be noted that, unlike theweighted bipartite graph. In this paper, we obtain maximal downlink control scenario, in the uplink, the joint powerweighted matching of a bipartite graph by the following control/channel assignment is coupled, and our two-phaseprocedure [24]: approach is not optimal. However, this approach makes the Maximal Weighted Bipartite Matching Procedure control problem much more manageable. . Step 1: Start with an empty match, i.e., without any 5.1 Phase 1 of UL-MDCA: Distributed Power Control edge selected. for Uplink Scenario . Step 2: Find a maximum augmenting path for the For the system model considered in this paper, uplink current match. An augmenting path is a path with power control is significantly more complicated than edges alternate between matched and unmatched. downlink power control. In the downlink case, there is The score of an augmenting path is equal to the sum only one secondary transmitter, i.e., the BS, which interferes of weights of unmatched edges subtracted by the primary links. On the other hand, for the uplink case, sum of weights of matched edges. A maximum different CPEs act as different transmitters and interfere augmenting path is the one with the maximum with PRXs in different ways. score. If this score of the maximum augmenting path We assume that, for each uplink connection, as long as the is not positive, then finish as the current match is SINR (at BS) is above the required threshold of s , the maximal. Otherwise, go to Step 3. transmission rate is fixed at a predetermined value, i.e., . Step 3: Flip the maximum augmenting path obtained fðÞ ¼ r; r 0. In other words, we do not consider rate in Step 2, i.e., change unmatched edges of the path to adaptation for uplink transmissions in the cognitive net- matched and matched edges of the path to un- work. Therefore, maximizing uplink throughput is equiva- matched. Go back to Step 2 to find another lent to maximizing the number of uplink connections with maximum augmenting path and continue. satisfied SINR. We further assume that there is at most one
  7. 7. 354 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 9, NO. 3, MARCH 2010PTX-PRX link operating on each of the K channels. With CPE n is terminated, BS, acting as the master, transmits athese assumptions, we propose the following Uplink control message to ask CPE n þ 1 to start its powerDistributed Power Control (UL-DPU) process that is applied updating process.to one channel at a time. For channel c, c 2 f1; . . . Kg, let PTX Round 2: After all N CPEs have been processed, a finali be the primary transmitter that operates on channel c. The round of power updating is carried out as follows:UL-DPU process is carried out in two rounds as follows: min Round 1: The CPEs are considered one at a time, starting . PTX i keeps transmitting at power PNþ1 , i.e., thefrom CPE 1. CPE n and PTX i carry out a distributed power transmit power it obtains after carrying out dis-updating process in an iterative manner as follows: tributed power update with CPE N. . For each CPE n that has been able to achieve the . Initialization: Set the initial transmit power of CPE n required SINR of s , i.e., n 2 À c , BS measures its SINR s min to Pn;c ð0Þ and initial transmit power of PTX i to P p . when PTX i transmits at power PNþ1 and instructs Similar to the case of downlink control, the initial CPE n to carry out a final power update according to transmit power of CPE n is chosen small enough so that Pn;c ð0ÞGsp . s n;i;c 8 . Iterative Power Updating: At step k, PTX i and CPE n s s P s s n;c su if Pn;c su P s; update their transmit powers as s n;c n;c Pn;c ¼ s ð22Þ 0 s ( ) : if Pn;c su P s : n;c p min p p Pi;c ðk þ 1Þ ¼ max Pn ; Pi;c ðkÞ pu ; i;n;c ðkÞ ð19Þ s s Pn;c ðk þ 1Þ ¼ s Pn;c ðkÞ; Note that in (22), n;c is the SINR experienced at BS s when CPE n and PTX i transmit at powers Pn;c and min min where Pn is the minimum transmit power for PTX PNþ1 , respectively. i when it carries out power updating with CPE n. A pseudocode for the UL-DPU procedure is given in min We set P1 ¼ 0 and calculate Pn min (n 1) as Fig. 13. explained next. We state and prove the following important character- . Termination: At step k, the power updating process istics of the UL-DPU process: between CPE n and PTX i will terminate if at least min Proposition 4. Given that PTX i transmits at power PNþ1 , if one of the following conditions is true: CPE n 2 Àc is assigned channel c and transmits at power - The SINR at PRX i is below the required value of Pn;c 0, the corresponding SINR at BS is s . s p . In this case, the uplink connection between Proof. The poof follows directly from (22) and the fact CPE n and BS will not be supported. We then set that SINR at BS scales linearly with the transmit power of CPEs. u t min min Pnþ1 ¼ Pn : ð20Þ Proposition 5. For each channel c, no matter what CPE in the set À c is assigned the channel for uplink transmission, the UL-DPU procedure ensures that the SINR of the PTX-PRX link operating - The transmit power of either CPE n or PTX i on channel c is always above the required threshold of p . exceeds the maximum allowable value (of P s and P p , respectively) before CPE n can achieve Proof. First, as the initial transmit power of CPE n is chosen the required SINR. In this case, the uplink so that Pn;c ð0ÞGsp , from (7), we have i;n;c ð0Þ ! p . s n;i;c pu connection between CPE n and BS will not be Then, similar to the proof of Proposition 2, it can be min supported. We then set Pnþ1 according to (20). shown that during Round 1 of UL-DPU, the SINR of the - The SINR at BS (corresponding to the transmis- PTX-PRX link is always above the required threshold of sion from CPE n) reaches the required value of p . What we need to prove is that Round 2 of UL-DPU s . In this case, CPE n records its transmit power also ensures that the SINR of the PTX-PRX link to be s s Pn;c ¼ Pn;c ðkÞ, BS also remembers this CPE by above the required threshold. If CPE n, n 2 Àc , transmits including it into a set À c . We then update s on channel c at power Pn;c and PTX i transmits at power min PNþ1 , the SINR at PRX i is min p Pnþ1 ¼ Pi;c ðkÞ: ð21Þ pu PNþ1 Gpp min i;i;c PNþ1 Gpp min i;i;c i;n;c ¼ ¼ No þ Pn;c Gsp s n;i;c s No þ Pn;c su Gsp s n;i;c minNote that Pn is an operating parameter of PTX i. So n;cwhen the iteration terminated, BS needs to send a one-bit min PNþ1 Pn Gpp min i;i;c ¼ ð23Þupdate to PTX-PRX i to inform them about the outcome min s Pn No þ P s su Gsp n;c n;c n;i;cof the power updating process, i.e., whether the uplinkconnection from CPE n can be supported. Based on this Pn Gpp min i;i;c min ! min Pn s ;one-bit information, PTX i will set Pn according to No þ min PNþ1 Pn;c su Gsp s n;i;c n;ceither (20) or (21). After the power updating process of
  8. 8. HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION 355 min min where the last inequality follows from PNþ1 ! Pn . We bounded by NK. Therefore, the complexity of Phase 2 of further note that DL-MDCA and UL-MDCA is OðN 2 KÞ. If we combine the complexity of Phase 1 and Phase 2, the su Pn;c Gss s n;0;c overall complexity of both DL-MDCA and UL-MDCA n;c ¼ ð24Þ No þ PNþ1 Gps min i;0;c scales as OðN 2 KÞ. and 7 OTHER CONTROL ALGORITHMS Pn;c Gss s n;0;c s ; ð25Þ It can be noted that two basic components of the proposed No þ Pn Gps min i;0;c DL-MDCA and UL-MDCA schemes are the (limited) as it is assumed that CPE n can achieve its SINR cooperation from primary devices during the power updat- s constraint when transmitting at power Pn;c while PTX i is ing process in Phase 1 and the centralized maximal bipartite min transmitting at power Pn . Therefore, matching employed for channel assignment in Phase 2. We are interested in understanding the impacts of these two s No þ PNþ1 Gps min i;0;c min PNþ1 components in the overall performance of DL-MDCA and ; ð26Þ su n;c No þ Pn Gps min i;0;c min Pn UL-MDCA. To study these impacts, we consider the other min min control algorithms given below. where the last inequality follows from PNþ1 ! Pn . Substituting (26) into (23) gives us 7.1 Noncooperative, Simple Matching (NCSM) Algorithm PNþ1 Gpp min i;i;c Pn Gpp min i;i;c The NCSM algorithm can be used in both downlink and ! ! p : ð27Þ No þ Pn;c Gsp s n;i;c No þ Pn;c Gsp s n;i;c uplink scenarios. By noncooperative, we mean that during the power control process in Phase 1 (of either downlink or So, the proof is completed. u t uplink scenario), PTXs do not adjust their transmit power together with BS or CPEs. Instead, each PTX fixes its5.2 Phase 2 of UL-MDCA: Centralized Channel transmit power at the maximum value of P p . BS or a CPE Assignment for Uplink Scenario then tries to maximize its transmit power on each channel,In this phase, channel assignment is carried out in a subject to the SINR constraints of all cochannel PRXs. Bycentralized manner in the same way as it is done in Phase 2 simple matching, we mean that channel assignment inof DL-MDCA scheme (Section 4.3). In particular, a bipartite Phase 2 (of either downlink or uplink scenario) is carriedgraph is first constructed, and after that, maximal bipartite out in a simple manner. In particular, CPEs are processedmatching is applied to get the optimal channel allocation. one by one according to a random order. For each CPE that has not been assigned any channel, we just randomly pick one channel that this CPE can operate at (i.e., with SINR6 COMPLEXITY ANALYSIS FOR DL-MDCA AND greater than s ) and assign to it. UL-MDCA By comparing the performance of DL-MDCA or UL-Let us look at the complexity of DL-MDCA and UL-MDCA. MDCA to that of NCSM, we can see the combined impact ofFor both algorithms, we can separate the overall complexity having primary cooperation in Phase 1 and maximalinto that of Phase 1 and Phase 2. bipartite matching in Phase 2.6.1 Complexity of Phase 1 7.2 Noncooperative, Maximal Matching (NCMM)Consider the DL-DPU process for the downlink scenario. AlgorithmFor each channel, the number of power updating iterations The NCMM algorithm can be used in both downlink andis bounded and does not depend either on the number of uplink scenarios. Phase 1 of this NCMM scheme is similar tonodes in the cognitive network or the number of PTX-PRX that of NCSM scheme described above, i.e., there is nolinks (see Proposition 1). Therefore, the complexity of the cooperation from primary transmitters. On the other hand,DL-DPU process is OðKÞ, where K is the number of in Phase 2, maximal bipartite matching is employed forchannels in the system. optimal channel assignment. By comparing the performance Consider the UL-DPU process for the uplink scenario. of DL-MDCA or UL-MDCA to that of NCMM, we can see theAgain, for each channel and each CPE, the number of impact of having primary users’ cooperation in Phase 1.power updating iterations is upper bounded by a constant. 7.3 Limited-Cooperation, Simple Matching (LCSM)Therefore, the complexity of UL-DPU process is OðNKÞ. Algorithm6.2 Complexity of Phase 2 The LCSM algorithm can be used in both downlink and uplink scenarios. Phase 1 of this LCSM scheme is similar toThe complexity of Phase 2 of either DL-MDCA or UL- that of DL-MDCA or UL-MDCA, i.e., PTXs participate inMDCA is due to the bipartite matching process. As it is well the distributed power updating process described inknown in graph theories [24], the complexity is Section 4.2. On the other hand, for Phase 2, simple matchingOðjV j2 þ jV kEjÞ, where jV j is the number of vertices and scheme as described for NCSM is employed. By comparingjEj is the number of edges in the corresponding bipartite the performance of DL-MDCA or UL-MDCA to that ofgraph. The number of vertices in our problem is equivalent LCSM, we can see the impact of carrying out optimalto the number of CPEs, i.e., N. The number of edges is upper bipartite matching in Phase 2.
  9. 9. 356 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 9, NO. 3, MARCH 2010Fig. 3. Behavior, in terms of received SINR at CPEs and PRXs, when Fig. 4. Percentage gains in total downlink transmission rate for optimal,the distributed power control scheme is employed. DL-MDCA, LCSM, and NCMM, relative to NCSM. Number of primary links ¼ 5.7.4 Centralized Optimal Control AlgorithmIn this algorithm, primary and secondary users measure used in the power updating process (Section 4.2) isand report all channel conditions to one central node, e.g., ¼ 1:259 % 1 dB. In our simulation, we assume that onthe BS or a primary node. This central node then calculates each channel, there is at most one PTX-PRX link.and decides the transmit power levels for all the transmit- For the transmission rate function discussed in Sec-ters. In other words, centralized power control is carried out tion 3.5, we use the approximation in [25], i.e., fðÞ ¼ ð0:6Þ1=3 . in Phase 1. In phase 2, maximal bipartite matching is We obtained similar results for other approximations of theemployed for optimal channel assignment. rate function. 8.2 Behaviors of DL-MDCA—Downlink Scenario8 NUMERICAL RESULTS AND DISCUSSION Let us fist look at the behaviors of the distributed power8.1 Simulation Model updating process proposed in Section 4.2 (for downlinkWe consider a square service area of size 1;000 m  1;000 m scenario). In Fig. 3, we plot the SINRs experienced by a PRXin which a cognitive radio network is deployed. A BS is and different CPEs on a particular channel during adeployed at the center of the cell to serve a set of CPEs. The distributed power updating process. As can be seen, as PTXtotal number of CPEs is N ¼ 10. The number of PTX-PRX starts at its maximum transmit power, the initial SINR of thelinks is set to 5 and 10. All CPEs and PTXs are randomly PRX is much higher than the constrained value of 15 dB. Ondeployed across the entire service area with a uniform the other hand, the initial SINRs of all CPEs are very low.distribution. Then each PRX is deployed such that the offsets Then, when the power updating process is employed, theof its horizontal and vertical coordinates, relative to the SINR at PRX quickly converges to the target value, which iscoordinates of the corresponding PTX, are uniformly 16 dB in this case. Note that the SINR of PRX converges todistributed within the range [50 m, 100 m]. This deployment 16 dB instead of the constrained value of 15 dB due to the usemodel represents a practical scenario in the currently being of power scaling factor ¼ 1:259 % 1 dB. As can be seen indeveloped IEEE802.22 WRAN standard, which allows Fig. 3, the SINRs of CPEs increase gradually after eachcognitive BS and CPEs to share spectrum with short-ranged iteration. Some CPEs eventually see their SINRs cross theincumbent wireless microphone devices [3]. A sample cutoff value of 15 dB while others never do. In Fig. 3, it is alsonetwork, with 10 CPEs and 5 PTX-PRX links is given in Fig. 1. interesting to observe that some CPEs may start at lower We model an orthogonal frequency-division multiple initial SINRs, however, their SINRs grow quicker and surpassaccess (OFDMA) system in which the entire bandwidth isdivided into 48 subcarriers. Each subcarrier is regarded as that of other CPEs. This is due to the variations in channelone channel in our power control/channel allocation gains from BS and PTXs to different CPEs. We observed thatschemes. The fading channel is represented by a six-tap with the given simulation parameters, it took 5-20 iterationschannel, with exponential decay factor. Although there are for the power updating process to terminate.48 channels (subcarriers), we assume that only 10 of them 8.3 Performance of DL-MDCA—Downlinkare considered for sharing between primary and secondary Throughputnetworks. These 10 subcarriers are equally spaced within theavailable bandwidth. The path loss exponent is taken to be 4. In Figs. 4 and 5, we plot the percentage gains in the totalThe noise power density at each CPE is No ¼ À100 dBm. The downlink throughput of Optimal, DL-MDCA, NCMM, andrequired SINR for each CPE is s ¼ 15 dB. The required LCSM, relative to that of NCSM. Note that Optimal schemeSINR for each PRX is varied from 5 to 30 dB. The maximum is based on centralized control as discussed in Section 7.4.transmit power on each channel for BS and PTX is 50 mW. Fig. 4 is for the case when there are five PTX-PRX links andFor the distributed power updating process, we set the Fig. 5 is for 10 PTX-PRX links. As can be seen, theinitial transmit power for secondary nodes (BS or CPEs) to performance gain of DL-MDCA is very significant andbe 0.5 mW and for PTXs to be 50 mW. The scaling factor ranges from 60 to 160 percent. This shows the combined
  10. 10. HOANG ET AL.: POWER CONTROL AND CHANNEL ALLOCATION IN COGNITIVE RADIO NETWORKS WITH PRIMARY USERS’ COOPERATION 357Fig. 5. Percentage gains in total downlink transmission rate for optimal, Fig. 7. Percentage gains in number of CPEs served for DL-MDCA,DL-MDCA, LCSM, and NCMM, relative to NCSM. Number of primary LCSM, and NCMM, relative to NCSM. Number of primary links ¼ 10.links ¼ 10. Fig. 8. Average number of CPEs served in the downlink by the baseline scheme NCSM.Fig. 6. Percentage gains in number of CPEs served for DL-MDCA,LCSM, and NCMM, relative to NCSM. Number of primary links ¼ 5. significant performance gain for DL-MDCA. Moreover, thisimpacts of having PTXs participating in the power updating performance impact (of using maximal matching) is moreprocess in Phase 1 and carrying out maximal matching in prominent when the SINR constraint of PRXs increases.Phase 2. It can also be noted that optimal centralized control This is because when the SINR constraint of PRXs increases,scheme performs slightly better than DL-MDCA. However, the channel availability pattern varies more significantlyas discussed in Section 7.4, this optimal scheme requires across CPEs. That makes it important to carry out intelligentknowledge of all channel conditions for a central node to channel assignment, which is achieved with maximalcalculate and set the transmit power levels for all secondary bipartite matching.and primary transmitters. In Figs. 6 and 7, we plot the gains of DL-MDCA, When comparing the performance of DL-MDCA and NCMM, and LCSM, relative to that of NCSM, when theNCMM in Figs. 4 and 5, it is evident that having primary performance metric is the total number of CPEs served,user’s cooperation in Phase 1 is important when the SINR instead of the downlink throughput. This is equivalent toconstraint of PRXs is low. However, at high SINR constraint setting the rate function fðÞ ¼ 1; 8 ! s . As can be seen,for PRXs, there is not much gain obtained from PTXs’ the performance trends are similar to that of Figs. 4 and 5.cooperation. This effect is expected, as when the SINR However, the gains are less significant. This is because byrequirement of PRXs is low, PTXs can cooperate more by making fð:Þ a constant function, there are less variations inreducing their transmit powers. Also, from Figs. 4 and 5, it the system for the control schemes to exploit. For reference,can be observed that the cooperation from PTXs has more we plot the absolute number of CPEs served by the baselinepositive impact when the number of primary links increases NCSM scheme in Fig. 8.from 5 to 10. This is because with more primary links, it isimportant that PTXs adjust their power to reduce inter- 8.4 Performance of UL-MDCA—Uplink Throughputference caused to CPEs. In Figs. 9 and 10, we plot the percentage gain, in the number of When comparing the performance of DL-MDCA and uplink connections being supported, of Optimal, UL-MDCA,LCSM in Figs. 4 and 5, it can be noted that carrying out LCSM, and NCMM, relative to that of NCSM. Note that as wemaximal weighted bipartite matching in Phase 2 gives assume that all active uplinks operating at the same SINR
  11. 11. 358 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 9, NO. 3, MARCH 2010Fig. 9. Percentage gains in number of CPEs served for optimal,UL-MDCA, LCSM, and NCMM, relative to NCSM, in the uplink scenario.Number of primary links ¼ 5. Fig. 12. DL-DPU process for channel c.Fig. 10. Percentage gains in number of CPEs served for optimal,UL-MDCA, LCSM, and NCMM, relative to NCSM, in the uplink scenario. are similar to that for the downlink scenario. When there areNumber of primary links ¼ 10. five PTX-PRX links, the gain of UL-MDCA, relative to NCSM, is from 6 to 13 percent. However, when the number of PTX-PRX links is increased to 10, the gain becomes much more significant and ranges from 20 to 120 percent. We also note that, when there are more primary links, cooperation from primary nodes becomes much more beneficial to the cognitive network. This is evident by the performance gap between LCSM and NCMM in Fig. 10. It can also be observed that the performance of Optimal scheme is slightly better than that of UL-MDCA. However, as discussed in Section 7.4, this optimal scheme requires knowledge of all channel conditions for a central node to calculate and set the transmit power levels for all secondary and primary transmitters. For reference, we plot the absolute number of CPEs served by the baseline NCSM scheme in Fig. 11.Fig. 11. Average number of CPEs served in the uplink by the baselinescheme NCSM. 9 CONCLUSIONS In this paper, we consider the problem of maximizing the(equal to the minimum required SINR of s ), the percentage throughput of a cognitive radio network while protectinggain in number of active uplink connections is equivalent to primary users of the spectrum. For this, we propose two mixed distributed/centralized control schemes (for down-the percentage gain in the total uplink throughput. link and uplink scenarios) that require minimal cooperation As can be observed, the performance trends of between cognitive and primary devices. Numerical resultsUL-MDCA, LCSM, and NCMM for the uplink scenario show the desired behaviors of our proposed algorithms and
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